Correlation function of quasars in real and redshift space from the Sloan Digital Sky Survey Data Release 7

We analyse the quasar two-point correlation function (2pCF) within the redshift interval 0.8 < z < 2.2 using a sample of 52 303 quasars selected from the recent Sloan Digital Sky Survey Data Release 7. Our approach to the 2pCF uses the concept of a local Lorentz (Fermi) frame, for the determination of the distance between objects, and the permutation method of random catalogue generation. Assuming a spatially flat cosmological model with (Lambda) = 0.726, we have found that the real-space 2pCF is fitted well with the power-law model within the distance range 1 < Sigma < 35 h-1 Mpc with the correlation length r(0) = 5.85 +/- 0.33 h-1 Mpc and the slope gamma = 1.87 +/- 0.07. The redshift-space 2pCF is approximated with s(0) = 6.43 +/- 0.63 h-1 Mpc and gamma = 1.21 +/- 0.24 for 1 < s < 10 h-1 Mpc, and s(0) = 7.37 +/- 0.81 h-1 Mpc and gamma = 1.90 +/- 0.24 for 10 < s < 35 h-1 Mpc. For distances s > 10 h-1 Mpc, the parameter describing the large-scale infall to density inhomogeneities is beta = 0.63 +/- 0.10 with the linear bias b = 1.44 +/- 0.22, which marginally (within 2 Sigma) agrees with the linear theory of cosmological perturbations. We discuss possibilities to obtain a statistical estimate of the random component of quasar velocities (different from the large-scale infall). We note a slight dependence of the quasar velocity dispersion upon the 2pCF parameters in the region r < 2 Mpc.